It might. Modern pharmaceutical research, for instance, is heavily, heavily gated by a number of agencies, policies, agendas, and so on. The idea that colonizing Mars would actually slow us down on that front really isn't hard to believe.
but that doesn't mean smaller countries with less string attached to research advance any faster
That's exactly what it means. Otherwise China and India would be the most advanced countries on the planet, or at absolute worst tied. They're not, largely because they've historically been too preoccupied with internal bullshit to advance their scientific understanding of the world very well. In fact, purely coincidentally I'm sure, they're some of the
most stereotypically "still has isolated semimedieval villages and vast swathes of poverty" places in the world.
What if you had to 'research' tech twice, oncee to discover them, and once on each planet (at a tiny fraction of the cost) to implement them there? Basically, like building buildings, but with a cost in research point?
A lot of techs lack a social cost anyway.
Well, explicitly. You can still assume Warship Engines Tier 2 have a social cost in that putting them on your ships requires putting them everywhere so that your entire empire is set up to produce fuel, parts, expertise, and so on. At that point getting every vehicle in your empire to switch engines and every power plant to produce different batteries and every mechanic to completely retrain themselves and so on makes sense as an ordeal.
Well, it would represent the cost of training the planet in the use of the new tech.
Maybe that's money or influence... more research points is thematically the wrong cost.
Research is probably thematically the closest you'll get in a single resource, as it represents figuring out how things work. Figuring out how to slot a new invention into the current system in such a way that it actually gets used is probably the most reasonable approximation of trying to introduce a New Thing.
Credits work if you're literally bribing everyone, paying for everyone's training, or losing raw income from the disruption, all of which require a somewhat more coherent and powerful government than you can probably expect from even an effective dictatorship (an ineffective one can probably just make it so, but nothing tends to work right in those at the best of times so I don't think you're gaining ground that way). Same issue with minerals, plus the fact that material renovations are only part of the problem.
Influence works pretty well because it's your go-to "this is what we're doing now" resource, but I don't think it's supposed to be cleared out periodically like that.